LMFDB - Embedded newform 2013.4.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$118.770844842$
Analytic rank:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41755 q^{2} +3.00000 q^{3} -5.99056 q^{4} +8.60687 q^{5} -4.25264 q^{6} +2.21724 q^{7} +19.8323 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.41755 q^{2} +3.00000 q^{3} -5.99056 q^{4} +8.60687 q^{5} -4.25264 q^{6} +2.21724 q^{7} +19.8323 q^{8} +9.00000 q^{9} -12.2006 q^{10} -11.0000 q^{11} -17.9717 q^{12} -62.2192 q^{13} -3.14304 q^{14} +25.8206 q^{15} +19.8114 q^{16} +59.5520 q^{17} -12.7579 q^{18} +65.5614 q^{19} -51.5600 q^{20} +6.65173 q^{21} +15.5930 q^{22} +2.75127 q^{23} +59.4968 q^{24} -50.9217 q^{25} +88.1986 q^{26} +27.0000 q^{27} -13.2825 q^{28} -266.886 q^{29} -36.6019 q^{30} +81.9533 q^{31} -186.742 q^{32} -33.0000 q^{33} -84.4176 q^{34} +19.0835 q^{35} -53.9151 q^{36} -82.5421 q^{37} -92.9362 q^{38} -186.658 q^{39} +170.694 q^{40} +424.877 q^{41} -9.42913 q^{42} -332.676 q^{43} +65.8962 q^{44} +77.4619 q^{45} -3.90005 q^{46} +409.247 q^{47} +59.4341 q^{48} -338.084 q^{49} +72.1839 q^{50} +178.656 q^{51} +372.728 q^{52} +331.072 q^{53} -38.2737 q^{54} -94.6756 q^{55} +43.9729 q^{56} +196.684 q^{57} +378.322 q^{58} -700.673 q^{59} -154.680 q^{60} -61.0000 q^{61} -116.172 q^{62} +19.9552 q^{63} +106.224 q^{64} -535.513 q^{65} +46.7790 q^{66} -520.904 q^{67} -356.750 q^{68} +8.25381 q^{69} -27.0518 q^{70} +582.731 q^{71} +178.490 q^{72} +526.774 q^{73} +117.007 q^{74} -152.765 q^{75} -392.750 q^{76} -24.3897 q^{77} +264.596 q^{78} -1176.29 q^{79} +170.514 q^{80} +81.0000 q^{81} -602.283 q^{82} -161.887 q^{83} -39.8476 q^{84} +512.556 q^{85} +471.584 q^{86} -800.657 q^{87} -218.155 q^{88} -982.716 q^{89} -109.806 q^{90} -137.955 q^{91} -16.4817 q^{92} +245.860 q^{93} -580.126 q^{94} +564.278 q^{95} -560.225 q^{96} -1405.93 q^{97} +479.249 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9}+O(q^{10}) $ 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9	\( 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9} - 41 q^{10} - 407 q^{11} + 390 q^{12} + 51 q^{13} - 228 q^{14} - 105 q^{15} + 462 q^{16} - 190 q^{17} - 72 q^{18} - 51 q^{19} - 720 q^{20} - 105 q^{21} + 88 q^{22} - 583 q^{23} - 351 q^{24} + 598 q^{25} - 1019 q^{26} + 999 q^{27} - 498 q^{28} - 566 q^{29} - 123 q^{30} - 696 q^{31} - 859 q^{32} - 1221 q^{33} - 348 q^{34} - 1102 q^{35} + 1170 q^{36} - 1022 q^{37} - 455 q^{38} + 153 q^{39} - 503 q^{40} - 790 q^{41} - 684 q^{42} - 87 q^{43} - 1430 q^{44} - 315 q^{45} - 303 q^{46} - 1603 q^{47} + 1386 q^{48} + 110 q^{49} - 1926 q^{50} - 570 q^{51} + 736 q^{52} - 2619 q^{53} - 216 q^{54} + 385 q^{55} - 4937 q^{56} - 153 q^{57} - 1099 q^{58} - 2471 q^{59} - 2160 q^{60} - 2257 q^{61} - 2909 q^{62} - 315 q^{63} - 265 q^{64} - 1970 q^{65} + 264 q^{66} - 3033 q^{67} - 1956 q^{68} - 1749 q^{69} + 2410 q^{70} - 3891 q^{71} - 1053 q^{72} + 391 q^{73} - 532 q^{74} + 1794 q^{75} + 1554 q^{76} + 385 q^{77} - 3057 q^{78} + 67 q^{79} - 5111 q^{80} + 2997 q^{81} - 4818 q^{82} - 5315 q^{83} - 1494 q^{84} - 2747 q^{85} - 5195 q^{86} - 1698 q^{87} + 1287 q^{88} - 8945 q^{89} - 369 q^{90} - 4432 q^{91} - 4701 q^{92} - 2088 q^{93} - 372 q^{94} - 3388 q^{95} - 2577 q^{96} - 3784 q^{97} - 4502 q^{98} - 3663 q^{99}+O(q^{100}) \) 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9 - 41 * q^10 - 407 * q^11 + 390 * q^12 + 51 * q^13 - 228 * q^14 - 105 * q^15 + 462 * q^16 - 190 * q^17 - 72 * q^18 - 51 * q^19 - 720 * q^20 - 105 * q^21 + 88 * q^22 - 583 * q^23 - 351 * q^24 + 598 * q^25 - 1019 * q^26 + 999 * q^27 - 498 * q^28 - 566 * q^29 - 123 * q^30 - 696 * q^31 - 859 * q^32 - 1221 * q^33 - 348 * q^34 - 1102 * q^35 + 1170 * q^36 - 1022 * q^37 - 455 * q^38 + 153 * q^39 - 503 * q^40 - 790 * q^41 - 684 * q^42 - 87 * q^43 - 1430 * q^44 - 315 * q^45 - 303 * q^46 - 1603 * q^47 + 1386 * q^48 + 110 * q^49 - 1926 * q^50 - 570 * q^51 + 736 * q^52 - 2619 * q^53 - 216 * q^54 + 385 * q^55 - 4937 * q^56 - 153 * q^57 - 1099 * q^58 - 2471 * q^59 - 2160 * q^60 - 2257 * q^61 - 2909 * q^62 - 315 * q^63 - 265 * q^64 - 1970 * q^65 + 264 * q^66 - 3033 * q^67 - 1956 * q^68 - 1749 * q^69 + 2410 * q^70 - 3891 * q^71 - 1053 * q^72 + 391 * q^73 - 532 * q^74 + 1794 * q^75 + 1554 * q^76 + 385 * q^77 - 3057 * q^78 + 67 * q^79 - 5111 * q^80 + 2997 * q^81 - 4818 * q^82 - 5315 * q^83 - 1494 * q^84 - 2747 * q^85 - 5195 * q^86 - 1698 * q^87 + 1287 * q^88 - 8945 * q^89 - 369 * q^90 - 4432 * q^91 - 4701 * q^92 - 2088 * q^93 - 372 * q^94 - 3388 * q^95 - 2577 * q^96 - 3784 * q^97 - 4502 * q^98 - 3663 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.41755	−0.501178	−0.250589	−	0.968094i	$-0.580624\pi$
$2$	−1.41755	−0.501178	−0.250589	+	0.968094i	$0.580624\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−5.99056	−0.748821
$5$	8.60687	0.769822	0.384911	−	0.922954i	$-0.374232\pi$
$5$	8.60687	0.769822	0.384911	+	0.922954i	$0.374232\pi$
$6$	−4.25264	−0.289355
$7$	2.21724	0.119720	0.0598599	−	0.998207i	$-0.480935\pi$
$7$	2.21724	0.119720	0.0598599	+	0.998207i	$0.480935\pi$
$8$	19.8323	0.876470
$9$	9.00000	0.333333
$10$	−12.2006	−0.385818
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−17.9717	−0.432332
$13$	−62.2192	−1.32742	−0.663712	−	0.747989i	$-0.731020\pi$
$13$	−62.2192	−1.32742	−0.663712	+	0.747989i	$0.731020\pi$
$14$	−3.14304	−0.0600009
$15$	25.8206	0.444457
$16$	19.8114	0.309553
$17$	59.5520	0.849616	0.424808	−	0.905283i	$-0.360342\pi$
$17$	59.5520	0.849616	0.424808	+	0.905283i	$0.360342\pi$
$18$	−12.7579	−0.167059
$19$	65.5614	0.791622	0.395811	−	0.918332i	$-0.370464\pi$
$19$	65.5614	0.791622	0.395811	+	0.918332i	$0.370464\pi$
$20$	−51.5600	−0.576459
$21$	6.65173	0.0691203
$22$	15.5930	0.151111
$23$	2.75127	0.0249426	0.0124713	−	0.999922i	$-0.496030\pi$
$23$	2.75127	0.0249426	0.0124713	+	0.999922i	$0.496030\pi$
$24$	59.4968	0.506030
$25$	−50.9217	−0.407374
$26$	88.1986	0.665275
$27$	27.0000	0.192450
$28$	−13.2825	−0.0896487
$29$	−266.886	−1.70894	−0.854472	−	0.519497i	$-0.826119\pi$
$29$	−266.886	−1.70894	−0.854472	+	0.519497i	$0.826119\pi$
$30$	−36.6019	−0.222752
$31$	81.9533	0.474814	0.237407	−	0.971410i	$-0.423702\pi$
$31$	81.9533	0.474814	0.237407	+	0.971410i	$0.423702\pi$
$32$	−186.742	−1.03161
$33$	−33.0000	−0.174078
$34$	−84.4176	−0.425809
$35$	19.0835	0.0921630
$36$	−53.9151	−0.249607
$37$	−82.5421	−0.366752	−0.183376	−	0.983043i	$-0.558703\pi$
$37$	−82.5421	−0.366752	−0.183376	+	0.983043i	$0.558703\pi$
$38$	−92.9362	−0.396743
$39$	−186.658	−0.766388
$40$	170.694	0.674726
$41$	424.877	1.61841	0.809203	−	0.587529i	$-0.199899\pi$
$41$	424.877	1.61841	0.809203	+	0.587529i	$0.199899\pi$
$42$	−9.42913	−0.0346416
$43$	−332.676	−1.17983	−0.589915	−	0.807465i	$-0.700839\pi$
$43$	−332.676	−1.17983	−0.589915	+	0.807465i	$0.700839\pi$
$44$	65.8962	0.225778
$45$	77.4619	0.256607
$46$	−3.90005	−0.0125007
$47$	409.247	1.27010	0.635051	−	0.772470i	$-0.280979\pi$
$47$	409.247	1.27010	0.635051	+	0.772470i	$0.280979\pi$
$48$	59.4341	0.178720
$49$	−338.084	−0.985667
$50$	72.1839	0.204167
$51$	178.656	0.490526
$52$	372.728	0.994002
$53$	331.072	0.858042	0.429021	−	0.903295i	$-0.358859\pi$
$53$	331.072	0.858042	0.429021	+	0.903295i	$0.358859\pi$
$54$	−38.2737	−0.0964518
$55$	−94.6756	−0.232110
$56$	43.9729	0.104931
$57$	196.684	0.457043
$58$	378.322	0.856486
$59$	−700.673	−1.54610	−0.773050	−	0.634346i	$-0.781270\pi$
$59$	−700.673	−1.54610	−0.773050	+	0.634346i	$0.781270\pi$
$60$	−154.680	−0.332819
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	−116.172	−0.237966
$63$	19.9552	0.0399066
$64$	106.224	0.207468
$65$	−535.513	−1.02188
$66$	46.7790	0.0872439
$67$	−520.904	−0.949829	−0.474915	−	0.880032i	$-0.657521\pi$
$67$	−520.904	−0.949829	−0.474915	+	0.880032i	$0.657521\pi$
$68$	−356.750	−0.636210
$69$	8.25381	0.0144006
$70$	−27.0518	−0.0461901
$71$	582.731	0.974048	0.487024	−	0.873388i	$-0.338082\pi$
$71$	582.731	0.974048	0.487024	+	0.873388i	$0.338082\pi$
$72$	178.490	0.292157
$73$	526.774	0.844578	0.422289	−	0.906461i	$-0.361227\pi$
$73$	526.774	0.844578	0.422289	+	0.906461i	$0.361227\pi$
$74$	117.007	0.183808
$75$	−152.765	−0.235197
$76$	−392.750	−0.592783
$77$	−24.3897	−0.0360969
$78$	264.596	0.384097
$79$	−1176.29	−1.67523	−0.837615	−	0.546261i	$-0.816051\pi$
$79$	−1176.29	−1.67523	−0.837615	+	0.546261i	$0.816051\pi$
$80$	170.514	0.238301
$81$	81.0000	0.111111
$82$	−602.283	−0.811110
$83$	−161.887	−0.214089	−0.107045	−	0.994254i	$-0.534139\pi$
$83$	−161.887	−0.214089	−0.107045	+	0.994254i	$0.534139\pi$
$84$	−39.8476	−0.0517587
$85$	512.556	0.654053
$86$	471.584	0.591305
$87$	−800.657	−0.986660
$88$	−218.155	−0.264266
$89$	−982.716	−1.17042	−0.585212	−	0.810880i	$-0.698989\pi$
$89$	−982.716	−1.17042	−0.585212	+	0.810880i	$0.698989\pi$
$90$	−109.806	−0.128606
$91$	−137.955	−0.158919
$92$	−16.4817	−0.0186775
$93$	245.860	0.274134
$94$	−580.126	−0.636548
$95$	564.278	0.609408
$96$	−560.225	−0.595601
$97$	−1405.93	−1.47165	−0.735826	−	0.677170i	$-0.763206\pi$
$97$	−1405.93	−1.47165	−0.735826	+	0.677170i	$0.763206\pi$
$98$	479.249	0.493995
$99$	−99.0000	−0.100504
$100$	305.050	0.305050
$101$	−99.6262	−0.0981503	−0.0490752	−	0.998795i	$-0.515627\pi$
$101$	−99.6262	−0.0981503	−0.0490752	+	0.998795i	$0.515627\pi$
$102$	−253.253	−0.245841
$103$	−1085.56	−1.03848	−0.519239	−	0.854629i	$-0.673785\pi$
$103$	−1085.56	−1.03848	−0.519239	+	0.854629i	$0.673785\pi$
$104$	−1233.95	−1.16345
$105$	57.2506	0.0532103
$106$	−469.309	−0.430032
$107$	2121.98	1.91719	0.958596	−	0.284769i	$-0.0919168\pi$
$107$	2121.98	1.91719	0.958596	+	0.284769i	$0.0919168\pi$
$108$	−161.745	−0.144111
$109$	1613.00	1.41741	0.708705	−	0.705504i	$-0.249280\pi$
$109$	1613.00	1.41741	0.708705	+	0.705504i	$0.249280\pi$
$110$	134.207	0.116329
$111$	−247.626	−0.211744
$112$	43.9266	0.0370596
$113$	587.456	0.489055	0.244527	−	0.969642i	$-0.421367\pi$
$113$	587.456	0.489055	0.244527	+	0.969642i	$0.421367\pi$
$114$	−278.809	−0.229060
$115$	23.6798	0.0192014
$116$	1598.79	1.27969
$117$	−559.973	−0.442474
$118$	993.236	0.774871
$119$	132.041	0.101716
$120$	512.081	0.389553
$121$	121.000	0.0909091
$122$	86.4703	0.0641693
$123$	1274.63	0.934388
$124$	−490.946	−0.355551
$125$	−1514.14	−1.08343
$126$	−28.2874	−0.0200003
$127$	−921.457	−0.643827	−0.321914	−	0.946769i	$-0.604326\pi$
$127$	−921.457	−0.643827	−0.321914	+	0.946769i	$0.604326\pi$
$128$	1343.36	0.927633
$129$	−998.029	−0.681175
$130$	759.114	0.512144
$131$	2558.54	1.70642	0.853210	−	0.521568i	$-0.174653\pi$
$131$	2558.54	1.70642	0.853210	+	0.521568i	$0.174653\pi$
$132$	197.689	0.130353
$133$	145.365	0.0947728
$134$	738.405	0.476034
$135$	232.386	0.148152
$136$	1181.05	0.744663
$137$	1814.55	1.13159	0.565794	−	0.824547i	$-0.308570\pi$
$137$	1814.55	1.13159	0.565794	+	0.824547i	$0.308570\pi$
$138$	−11.7002	−0.00721727
$139$	379.388	0.231506	0.115753	−	0.993278i	$-0.463072\pi$
$139$	379.388	0.231506	0.115753	+	0.993278i	$0.463072\pi$
$140$	−114.321	−0.0690135
$141$	1227.74	0.733294
$142$	−826.048	−0.488172
$143$	684.411	0.400233
$144$	178.302	0.103184
$145$	−2297.05	−1.31558
$146$	−746.726	−0.423284
$147$	−1014.25	−0.569075
$148$	494.474	0.274632
$149$	−3108.70	−1.70923	−0.854613	−	0.519265i	$-0.826206\pi$
$149$	−3108.70	−1.70923	−0.854613	+	0.519265i	$0.826206\pi$
$150$	216.552	0.117876
$151$	−2365.52	−1.27486	−0.637428	−	0.770510i	$-0.720002\pi$
$151$	−2365.52	−1.27486	−0.637428	+	0.770510i	$0.720002\pi$
$152$	1300.23	0.693833
$153$	535.968	0.283205
$154$	34.5735	0.0180910
$155$	705.362	0.365523
$156$	1118.18	0.573887
$157$	−444.919	−0.226168	−0.113084	−	0.993585i	$-0.536073\pi$
$157$	−444.919	−0.226168	−0.113084	+	0.993585i	$0.536073\pi$
$158$	1667.45	0.839588
$159$	993.216	0.495391
$160$	−1607.26	−0.794157
$161$	6.10023	0.00298612
$162$	−114.821	−0.0556864
$163$	−534.546	−0.256864	−0.128432	−	0.991718i	$-0.540994\pi$
$163$	−534.546	−0.256864	−0.128432	+	0.991718i	$0.540994\pi$
$164$	−2545.25	−1.21190
$165$	−284.027	−0.134009
$166$	229.482	0.107297
$167$	−1364.17	−0.632111	−0.316056	−	0.948741i	$-0.602359\pi$
$167$	−1364.17	−0.632111	−0.316056	+	0.948741i	$0.602359\pi$
$168$	131.919	0.0605819
$169$	1674.23	0.762053
$170$	−726.572	−0.327797
$171$	590.052	0.263874
$172$	1992.92	0.883481
$173$	−915.759	−0.402450	−0.201225	−	0.979545i	$-0.564492\pi$
$173$	−915.759	−0.402450	−0.201225	+	0.979545i	$0.564492\pi$
$174$	1134.97	0.494492
$175$	−112.906	−0.0487707
$176$	−217.925	−0.0933337
$177$	−2102.02	−0.892641
$178$	1393.05	0.586591
$179$	−862.762	−0.360256	−0.180128	−	0.983643i	$-0.557651\pi$
$179$	−862.762	−0.360256	−0.180128	+	0.983643i	$0.557651\pi$
$180$	−464.040	−0.192153
$181$	964.242	0.395975	0.197988	−	0.980205i	$-0.436559\pi$
$181$	964.242	0.395975	0.197988	+	0.980205i	$0.436559\pi$
$182$	195.558	0.0796467
$183$	−183.000	−0.0739221
$184$	54.5639	0.0218614
$185$	−710.429	−0.282334
$186$	−348.517	−0.137390
$187$	−655.072	−0.256169
$188$	−2451.62	−0.951079
$189$	59.8655	0.0230401
$190$	−799.890	−0.305422
$191$	−801.257	−0.303544	−0.151772	−	0.988416i	$-0.548498\pi$
$191$	−801.257	−0.303544	−0.151772	+	0.988416i	$0.548498\pi$
$192$	318.671	0.119782
$193$	−2952.56	−1.10119	−0.550596	−	0.834772i	$-0.685600\pi$
$193$	−2952.56	−1.10119	−0.550596	+	0.834772i	$0.685600\pi$
$194$	1992.97	0.737560
$195$	−1606.54	−0.589983
$196$	2025.31	0.738088
$197$	−294.397	−0.106472	−0.0532358	−	0.998582i	$-0.516953\pi$
$197$	−294.397	−0.106472	−0.0532358	+	0.998582i	$0.516953\pi$
$198$	140.337	0.0503703
$199$	2933.79	1.04508	0.522540	−	0.852615i	$-0.324985\pi$
$199$	2933.79	1.04508	0.522540	+	0.852615i	$0.324985\pi$
$200$	−1009.89	−0.357051
$201$	−1562.71	−0.548384
$202$	141.225	0.0491908
$203$	−591.750	−0.204595
$204$	−1070.25	−0.367316
$205$	3656.87	1.24589
$206$	1538.83	0.520463
$207$	24.7614	0.00831420
$208$	−1232.65	−0.410908
$209$	−721.175	−0.238683
$210$	−81.1553	−0.0266678
$211$	447.085	0.145870	0.0729350	−	0.997337i	$-0.476763\pi$
$211$	447.085	0.145870	0.0729350	+	0.997337i	$0.476763\pi$
$212$	−1983.31	−0.642519
$213$	1748.19	0.562367
$214$	−3008.00	−0.960855
$215$	−2863.30	−0.908259
$216$	535.471	0.168677
$217$	181.710	0.0568447
$218$	−2286.51	−0.710375
$219$	1580.32	0.487617
$220$	567.160	0.173809
$221$	−3705.28	−1.12780
$222$	351.021	0.106122
$223$	3718.87	1.11674	0.558372	−	0.829591i	$-0.311426\pi$
$223$	3718.87	1.11674	0.558372	+	0.829591i	$0.311426\pi$
$224$	−414.051	−0.123504
$225$	−458.295	−0.135791
$226$	−832.745	−0.245103
$227$	−4854.84	−1.41950	−0.709751	−	0.704453i	$-0.751193\pi$
$227$	−4854.84	−1.41950	−0.709751	+	0.704453i	$0.751193\pi$
$228$	−1178.25	−0.342243
$229$	−2991.50	−0.863249	−0.431624	−	0.902053i	$-0.642059\pi$
$229$	−2991.50	−0.863249	−0.431624	+	0.902053i	$0.642059\pi$
$230$	−33.5672	−0.00962330
$231$	−73.1690	−0.0208405
$232$	−5292.94	−1.49784
$233$	−5431.80	−1.52725	−0.763625	−	0.645660i	$-0.776582\pi$
$233$	−5431.80	−1.52725	−0.763625	+	0.645660i	$0.776582\pi$
$234$	793.787	0.221758
$235$	3522.34	0.977753
$236$	4197.43	1.15775
$237$	−3528.87	−0.967194
$238$	−187.174	−0.0509778
$239$	5222.11	1.41335	0.706674	−	0.707540i	$-0.250195\pi$
$239$	5222.11	1.41335	0.706674	+	0.707540i	$0.250195\pi$
$240$	511.542	0.137583
$241$	−7047.23	−1.88362	−0.941810	−	0.336147i	$-0.890876\pi$
$241$	−7047.23	−1.88362	−0.941810	+	0.336147i	$0.890876\pi$
$242$	−171.523	−0.0455616
$243$	243.000	0.0641500
$244$	365.424	0.0958767
$245$	−2909.85	−0.758788
$246$	−1806.85	−0.468295
$247$	−4079.18	−1.05082
$248$	1625.32	0.416161
$249$	−485.661	−0.123605
$250$	2146.36	0.542990
$251$	−1801.78	−0.453097	−0.226549	−	0.974000i	$-0.572744\pi$
$251$	−1801.78	−0.453097	−0.226549	+	0.974000i	$0.572744\pi$
$252$	−119.543	−0.0298829
$253$	−30.2640	−0.00752047
$254$	1306.21	0.322672
$255$	1537.67	0.377618
$256$	−2754.06	−0.672378
$257$	68.3334	0.0165857	0.00829284	−	0.999966i	$-0.497360\pi$
$257$	68.3334	0.0165857	0.00829284	+	0.999966i	$0.497360\pi$
$258$	1414.75	0.341390
$259$	−183.016	−0.0439075
$260$	3208.02	0.765205
$261$	−2401.97	−0.569648
$262$	−3626.85	−0.855220
$263$	2537.00	0.594822	0.297411	−	0.954750i	$-0.403877\pi$
$263$	2537.00	0.594822	0.297411	+	0.954750i	$0.403877\pi$
$264$	−654.465	−0.152574
$265$	2849.49	0.660540
$266$	−206.062	−0.0474980
$267$	−2948.15	−0.675745
$268$	3120.51	0.711252
$269$	−4891.83	−1.10877	−0.554387	−	0.832259i	$-0.687047\pi$
$269$	−4891.83	−1.10877	−0.554387	+	0.832259i	$0.687047\pi$
$270$	−329.417	−0.0742507
$271$	3765.58	0.844070	0.422035	−	0.906580i	$-0.361316\pi$
$271$	3765.58	0.844070	0.422035	+	0.906580i	$0.361316\pi$
$272$	1179.81	0.263001
$273$	−413.865	−0.0917519
$274$	−2572.21	−0.567127
$275$	560.139	0.122828
$276$	−49.4450	−0.0107835
$277$	−1782.33	−0.386605	−0.193303	−	0.981139i	$-0.561920\pi$
$277$	−1782.33	−0.386605	−0.193303	+	0.981139i	$0.561920\pi$
$278$	−537.800	−0.116026
$279$	737.579	0.158271
$280$	378.469	0.0807781
$281$	6547.08	1.38992	0.694958	−	0.719051i	$-0.255423\pi$
$281$	6547.08	1.38992	0.694958	+	0.719051i	$0.255423\pi$
$282$	−1740.38	−0.367511
$283$	−1057.76	−0.222180	−0.111090	−	0.993810i	$-0.535434\pi$
$283$	−1057.76	−0.222180	−0.111090	+	0.993810i	$0.535434\pi$
$284$	−3490.89	−0.729387
$285$	1692.84	0.351842
$286$	−970.184	−0.200588
$287$	942.056	0.193755
$288$	−1680.67	−0.343871
$289$	−1366.56	−0.278153
$290$	3256.17	0.659342
$291$	−4217.78	−0.849659
$292$	−3155.67	−0.632437
$293$	−572.594	−0.114168	−0.0570841	−	0.998369i	$-0.518180\pi$
$293$	−572.594	−0.114168	−0.0570841	+	0.998369i	$0.518180\pi$
$294$	1437.75	0.285208
$295$	−6030.60	−1.19022
$296$	−1637.00	−0.321447
$297$	−297.000	−0.0580259
$298$	4406.73	0.856627
$299$	−171.182	−0.0331094
$300$	915.150	0.176121
$301$	−737.624	−0.141249
$302$	3353.23	0.638930
$303$	−298.879	−0.0566671
$304$	1298.86	0.245049
$305$	−525.019	−0.0985656
$306$	−759.759	−0.141936
$307$	−124.237	−0.0230964	−0.0115482	−	0.999933i	$-0.503676\pi$
$307$	−124.237	−0.0230964	−0.0115482	+	0.999933i	$0.503676\pi$
$308$	146.108	0.0270301
$309$	−3256.68	−0.599566
$310$	−999.882	−0.183192
$311$	−8867.24	−1.61677	−0.808385	−	0.588655i	$-0.799658\pi$
$311$	−8867.24	−1.61677	−0.808385	+	0.588655i	$0.799658\pi$
$312$	−3701.84	−0.671717
$313$	−7672.42	−1.38553	−0.692765	−	0.721163i	$-0.743608\pi$
$313$	−7672.42	−1.38553	−0.692765	+	0.721163i	$0.743608\pi$
$314$	630.693	0.113350
$315$	171.752	0.0307210
$316$	7046.65	1.25445
$317$	2193.44	0.388631	0.194316	−	0.980939i	$-0.437751\pi$
$317$	2193.44	0.388631	0.194316	+	0.980939i	$0.437751\pi$
$318$	−1407.93	−0.248279
$319$	2935.74	0.515266
$320$	914.254	0.159714
$321$	6365.94	1.10689
$322$	−8.64736	−0.00149658
$323$	3904.31	0.672574
$324$	−485.236	−0.0832023
$325$	3168.31	0.540757
$326$	757.743	0.128735
$327$	4839.01	0.818343
$328$	8426.28	1.41849
$329$	907.400	0.152056
$330$	402.621	0.0671623
$331$	−1123.54	−0.186572	−0.0932862	−	0.995639i	$-0.529737\pi$
$331$	−1123.54	−0.186572	−0.0932862	+	0.995639i	$0.529737\pi$
$332$	969.795	0.160315
$333$	−742.879	−0.122251
$334$	1933.77	0.316800
$335$	−4483.36	−0.731200
$336$	131.780	0.0213964
$337$	−7026.76	−1.13582	−0.567911	−	0.823090i	$-0.692248\pi$
$337$	−7026.76	−1.13582	−0.567911	+	0.823090i	$0.692248\pi$
$338$	−2373.30	−0.381924
$339$	1762.37	0.282356
$340$	−3070.50	−0.489769
$341$	−901.486	−0.143162
$342$	−836.426	−0.132248
$343$	−1510.13	−0.237724
$344$	−6597.73	−1.03409
$345$	71.0395	0.0110859
$346$	1298.13	0.201699
$347$	−6206.85	−0.960233	−0.480117	−	0.877205i	$-0.659406\pi$
$347$	−6206.85	−0.960233	−0.480117	+	0.877205i	$0.659406\pi$
$348$	4796.38	0.738831
$349$	1891.02	0.290041	0.145020	−	0.989429i	$-0.453675\pi$
$349$	1891.02	0.290041	0.145020	+	0.989429i	$0.453675\pi$
$350$	160.049	0.0244428
$351$	−1679.92	−0.255463
$352$	2054.16	0.311043
$353$	−9993.35	−1.50678	−0.753389	−	0.657576i	$-0.771582\pi$
$353$	−9993.35	−1.50678	−0.753389	+	0.657576i	$0.771582\pi$
$354$	2979.71	0.447372
$355$	5015.49	0.749844
$356$	5887.03	0.876437
$357$	396.123	0.0587257
$358$	1223.00	0.180552
$359$	−8967.63	−1.31837	−0.659183	−	0.751982i	$-0.729098\pi$
$359$	−8967.63	−1.31837	−0.659183	+	0.751982i	$0.729098\pi$
$360$	1536.24	0.224909
$361$	−2560.71	−0.373335
$362$	−1366.86	−0.198454
$363$	363.000	0.0524864
$364$	826.429	0.119002
$365$	4533.87	0.650175
$366$	259.411	0.0370481
$367$	5118.74	0.728055	0.364027	−	0.931388i	$-0.381401\pi$
$367$	5118.74	0.728055	0.364027	+	0.931388i	$0.381401\pi$
$368$	54.5065	0.00772105
$369$	3823.90	0.539469
$370$	1007.07	0.141500
$371$	734.067	0.102725
$372$	−1472.84	−0.205277
$373$	−8566.29	−1.18913	−0.594565	−	0.804047i	$-0.702676\pi$
$373$	−8566.29	−1.18913	−0.594565	+	0.804047i	$0.702676\pi$
$374$	928.594	0.128386
$375$	−4542.41	−0.625517
$376$	8116.30	1.11321
$377$	16605.4	2.26849
$378$	−84.8621	−0.0115472
$379$	2876.61	0.389872	0.194936	−	0.980816i	$-0.437550\pi$
$379$	2876.61	0.389872	0.194936	+	0.980816i	$0.437550\pi$
$380$	−3380.35	−0.456337
$381$	−2764.37	−0.371714
$382$	1135.82	0.152130
$383$	3375.42	0.450329	0.225165	−	0.974321i	$-0.427708\pi$
$383$	3375.42	0.450329	0.225165	+	0.974321i	$0.427708\pi$
$384$	4030.07	0.535569
$385$	−209.919	−0.0277882
$386$	4185.39	0.551894
$387$	−2994.09	−0.393277
$388$	8422.30	1.10200
$389$	−8372.18	−1.09122	−0.545612	−	0.838038i	$-0.683703\pi$
$389$	−8372.18	−1.09122	−0.545612	+	0.838038i	$0.683703\pi$
$390$	2277.34	0.295686
$391$	163.844	0.0211916
$392$	−6704.97	−0.863908
$393$	7675.63	0.985202
$394$	417.321	0.0533612
$395$	−10124.2	−1.28963
$396$	593.066	0.0752593
$397$	5007.64	0.633064	0.316532	−	0.948582i	$-0.397482\pi$
$397$	5007.64	0.633064	0.316532	+	0.948582i	$0.397482\pi$
$398$	−4158.78	−0.523771
$399$	436.096	0.0547171
$400$	−1008.83	−0.126104
$401$	−3281.80	−0.408692	−0.204346	−	0.978899i	$-0.565507\pi$
$401$	−3281.80	−0.408692	−0.204346	+	0.978899i	$0.565507\pi$
$402$	2215.22	0.274838
$403$	−5099.07	−0.630280
$404$	596.817	0.0734970
$405$	697.157	0.0855358
$406$	838.832	0.102538
$407$	907.963	0.110580
$408$	3543.15	0.429932
$409$	11721.4	1.41708	0.708539	−	0.705672i	$-0.249355\pi$
$409$	11721.4	1.41708	0.708539	+	0.705672i	$0.249355\pi$
$410$	−5183.77	−0.624410
$411$	5443.65	0.653322
$412$	6503.11	0.777634
$413$	−1553.56	−0.185099
$414$	−35.1005	−0.00416689
$415$	−1393.34	−0.164811
$416$	11618.9	1.36939
$417$	1138.16	0.133660
$418$	1022.30	0.119623
$419$	−7240.65	−0.844222	−0.422111	−	0.906544i	$-0.638711\pi$
$419$	−7240.65	−0.844222	−0.422111	+	0.906544i	$0.638711\pi$
$420$	−342.963	−0.0398450
$421$	−11337.6	−1.31249	−0.656245	−	0.754548i	$-0.727856\pi$
$421$	−11337.6	−1.31249	−0.656245	+	0.754548i	$0.727856\pi$
$422$	−633.763	−0.0731069
$423$	3683.22	0.423368
$424$	6565.90	0.752048
$425$	−3032.49	−0.346111
$426$	−2478.14	−0.281846
$427$	−135.252	−0.0153286
$428$	−12711.9	−1.43563
$429$	2053.23	0.231075
$430$	4058.86	0.455200
$431$	−16872.5	−1.88566	−0.942828	−	0.333279i	$-0.891845\pi$
$431$	−16872.5	−1.88566	−0.942828	+	0.333279i	$0.891845\pi$
$432$	534.907	0.0595735
$433$	−8360.93	−0.927947	−0.463973	−	0.885849i	$-0.653577\pi$
$433$	−8360.93	−0.927947	−0.463973	+	0.885849i	$0.653577\pi$
$434$	−257.583	−0.0284893
$435$	−6891.15	−0.759553
$436$	−9662.81	−1.06139
$437$	180.377	0.0197451
$438$	−2240.18	−0.244383
$439$	−6357.95	−0.691226	−0.345613	−	0.938377i	$-0.612329\pi$
$439$	−6357.95	−0.691226	−0.345613	+	0.938377i	$0.612329\pi$
$440$	−1877.63	−0.203438
$441$	−3042.75	−0.328556
$442$	5252.40	0.565229
$443$	−17007.9	−1.82408	−0.912040	−	0.410101i	$-0.865493\pi$
$443$	−17007.9	−1.82408	−0.912040	+	0.410101i	$0.865493\pi$
$444$	1483.42	0.158559
$445$	−8458.12	−0.901018
$446$	−5271.67	−0.559688
$447$	−9326.10	−0.986822
$448$	235.524	0.0248381
$449$	10419.9	1.09520	0.547600	−	0.836740i	$-0.315541\pi$
$449$	10419.9	1.09520	0.547600	+	0.836740i	$0.315541\pi$
$450$	649.655	0.0680556
$451$	−4673.65	−0.487968
$452$	−3519.19	−0.366214
$453$	−7096.56	−0.736039
$454$	6881.95	0.711423
$455$	−1187.36	−0.122339
$456$	3900.69	0.400585
$457$	365.621	0.0374246	0.0187123	−	0.999825i	$-0.494043\pi$
$457$	365.621	0.0374246	0.0187123	+	0.999825i	$0.494043\pi$
$458$	4240.59	0.432641
$459$	1607.90	0.163509
$460$	−141.856	−0.0143784
$461$	−6083.63	−0.614627	−0.307313	−	0.951608i	$-0.599430\pi$
$461$	−6083.63	−0.614627	−0.307313	+	0.951608i	$0.599430\pi$
$462$	103.720	0.0104448
$463$	−5313.60	−0.533356	−0.266678	−	0.963786i	$-0.585926\pi$
$463$	−5313.60	−0.533356	−0.266678	+	0.963786i	$0.585926\pi$
$464$	−5287.37	−0.529009
$465$	2116.08	0.211035
$466$	7699.82	0.765424
$467$	−9473.92	−0.938760	−0.469380	−	0.882996i	$-0.655523\pi$
$467$	−9473.92	−0.938760	−0.469380	+	0.882996i	$0.655523\pi$
$468$	3354.55	0.331334
$469$	−1154.97	−0.113713
$470$	−4993.07	−0.490028
$471$	−1334.76	−0.130578
$472$	−13895.9	−1.35511
$473$	3659.44	0.355732
$474$	5002.34	0.484736
$475$	−3338.50	−0.322486
$476$	−791.001	−0.0761669
$477$	2979.65	0.286014
$478$	−7402.58	−0.708339
$479$	9851.26	0.939698	0.469849	−	0.882747i	$-0.344308\pi$
$479$	9851.26	0.939698	0.469849	+	0.882747i	$0.344308\pi$
$480$	−4821.79	−0.458507
$481$	5135.70	0.486835
$482$	9989.77	0.944029
$483$	18.3007	0.00172404
$484$	−724.858	−0.0680746
$485$	−12100.6	−1.13291
$486$	−344.464	−0.0321506
$487$	58.9689	0.00548693	0.00274347	−	0.999996i	$-0.499127\pi$
$487$	58.9689	0.00548693	0.00274347	+	0.999996i	$0.499127\pi$
$488$	−1209.77	−0.112221
$489$	−1603.64	−0.148301
$490$	4124.84	0.380288
$491$	8578.66	0.788492	0.394246	−	0.919005i	$-0.371006\pi$
$491$	8578.66	0.788492	0.394246	+	0.919005i	$0.371006\pi$
$492$	−7635.76	−0.699689
$493$	−15893.6	−1.45195
$494$	5782.42	0.526646
$495$	−852.081	−0.0773700
$496$	1623.61	0.146980
$497$	1292.06	0.116613
$498$	688.447	0.0619479
$499$	−14625.2	−1.31205	−0.656025	−	0.754739i	$-0.727763\pi$
$499$	−14625.2	−1.31205	−0.656025	+	0.754739i	$0.727763\pi$
$500$	9070.53	0.811293
$501$	−4092.51	−0.364950
$502$	2554.11	0.227082
$503$	14470.0	1.28267	0.641337	−	0.767259i	$-0.278380\pi$
$503$	14470.0	1.28267	0.641337	+	0.767259i	$0.278380\pi$
$504$	395.756	0.0349770
$505$	−857.471	−0.0755583
$506$	42.9006	0.00376910
$507$	5022.69	0.439971
$508$	5520.05	0.482111
$509$	16551.8	1.44135	0.720673	−	0.693275i	$-0.243833\pi$
$509$	16551.8	1.44135	0.720673	+	0.693275i	$0.243833\pi$
$510$	−2179.72	−0.189254
$511$	1167.98	0.101113
$512$	−6842.85	−0.590652
$513$	1770.16	0.152348
$514$	−96.8657	−0.00831238
$515$	−9343.27	−0.799444
$516$	5978.76	0.510078
$517$	−4501.72	−0.382950
$518$	259.433	0.0220055
$519$	−2747.28	−0.232355
$520$	−10620.4	−0.895648
$521$	4319.15	0.363197	0.181598	−	0.983373i	$-0.441873\pi$
$521$	4319.15	0.363197	0.181598	+	0.983373i	$0.441873\pi$
$522$	3404.90	0.285495
$523$	10258.6	0.857698	0.428849	−	0.903376i	$-0.358919\pi$
$523$	10258.6	0.857698	0.428849	+	0.903376i	$0.358919\pi$
$524$	−15327.1	−1.27780
$525$	−338.717	−0.0281578
$526$	−3596.32	−0.298112
$527$	4880.48	0.403410
$528$	−653.776	−0.0538862
$529$	−12159.4	−0.999378
$530$	−4039.29	−0.331048
$531$	−6306.06	−0.515366
$532$	−870.821	−0.0709678
$533$	−26435.5	−2.14831
$534$	4179.14	0.338668
$535$	18263.6	1.47590
$536$	−10330.7	−0.832497
$537$	−2588.28	−0.207994
$538$	6934.39	0.555693
$539$	3718.92	0.297190
$540$	−1392.12	−0.110940
$541$	−3972.76	−0.315716	−0.157858	−	0.987462i	$-0.550459\pi$
$541$	−3972.76	−0.315716	−0.157858	+	0.987462i	$0.550459\pi$
$542$	−5337.88	−0.423029
$543$	2892.73	0.228616
$544$	−11120.8	−0.876474
$545$	13882.9	1.09115
$546$	586.673	0.0459840
$547$	19380.4	1.51489	0.757446	−	0.652898i	$-0.226447\pi$
$547$	19380.4	1.51489	0.757446	+	0.652898i	$0.226447\pi$
$548$	−10870.2	−0.847356
$549$	−549.000	−0.0426790
$550$	−794.022	−0.0615586
$551$	−17497.4	−1.35284
$552$	163.692	0.0126217
$553$	−2608.12	−0.200558
$554$	2526.53	0.193758
$555$	−2131.29	−0.163006
$556$	−2272.75	−0.173356
$557$	−14875.2	−1.13157	−0.565785	−	0.824553i	$-0.691427\pi$
$557$	−14875.2	−1.13157	−0.565785	+	0.824553i	$0.691427\pi$
$558$	−1045.55	−0.0793222
$559$	20698.9	1.56613
$560$	378.071	0.0285293
$561$	−1965.21	−0.147899
$562$	−9280.79	−0.696595
$563$	−4287.65	−0.320964	−0.160482	−	0.987039i	$-0.551305\pi$
$563$	−4287.65	−0.320964	−0.160482	+	0.987039i	$0.551305\pi$
$564$	−7354.86	−0.549106
$565$	5056.16	0.376485
$566$	1499.42	0.111352
$567$	179.597	0.0133022
$568$	11556.9	0.853725
$569$	26012.9	1.91655	0.958277	−	0.285842i	$-0.0922731\pi$
$569$	26012.9	1.91655	0.958277	+	0.285842i	$0.0922731\pi$
$570$	−2399.67	−0.176335
$571$	3047.93	0.223383	0.111692	−	0.993743i	$-0.464373\pi$
$571$	3047.93	0.223383	0.111692	+	0.993743i	$0.464373\pi$
$572$	−4100.01	−0.299703
$573$	−2403.77	−0.175251
$574$	−1335.41	−0.0971059
$575$	−140.099	−0.0101610
$576$	956.014	0.0691561
$577$	16099.6	1.16158	0.580792	−	0.814052i	$-0.302743\pi$
$577$	16099.6	1.16158	0.580792	+	0.814052i	$0.302743\pi$
$578$	1937.17	0.139404
$579$	−8857.69	−0.635774
$580$	13760.6	0.985136
$581$	−358.943	−0.0256307
$582$	5978.90	0.425830
$583$	−3641.79	−0.258709
$584$	10447.1	0.740248
$585$	−4819.62	−0.340627
$586$	811.678	0.0572186
$587$	−9568.57	−0.672806	−0.336403	−	0.941718i	$-0.609210\pi$
$587$	−9568.57	−0.672806	−0.336403	+	0.941718i	$0.609210\pi$
$588$	6075.94	0.426135
$589$	5372.97	0.375873
$590$	8548.66	0.596513
$591$	−883.190	−0.0614714
$592$	−1635.27	−0.113529
$593$	3074.58	0.212914	0.106457	−	0.994317i	$-0.466049\pi$
$593$	3074.58	0.212914	0.106457	+	0.994317i	$0.466049\pi$
$594$	421.011	0.0290813
$595$	1136.46	0.0783031
$596$	18622.9	1.27990
$597$	8801.37	0.603377
$598$	242.658	0.0165937
$599$	−3185.21	−0.217269	−0.108635	−	0.994082i	$-0.534648\pi$
$599$	−3185.21	−0.217269	−0.108635	+	0.994082i	$0.534648\pi$
$600$	−3029.68	−0.206144
$601$	1976.09	0.134120	0.0670602	−	0.997749i	$-0.478638\pi$
$601$	1976.09	0.134120	0.0670602	+	0.997749i	$0.478638\pi$
$602$	1045.62	0.0707909
$603$	−4688.14	−0.316610
$604$	14170.8	0.954638
$605$	1041.43	0.0699838
$606$	423.674	0.0284003
$607$	5411.80	0.361875	0.180938	−	0.983495i	$-0.442087\pi$
$607$	5411.80	0.361875	0.180938	+	0.983495i	$0.442087\pi$
$608$	−12243.0	−0.816646
$609$	−1775.25	−0.118123
$610$	744.239	0.0493989
$611$	−25463.0	−1.68596
$612$	−3210.75	−0.212070
$613$	16851.6	1.11033	0.555164	−	0.831741i	$-0.312656\pi$
$613$	16851.6	1.11033	0.555164	+	0.831741i	$0.312656\pi$
$614$	176.112	0.0115754
$615$	10970.6	0.719312
$616$	−483.702	−0.0316379
$617$	5745.45	0.374883	0.187442	−	0.982276i	$-0.439980\pi$
$617$	5745.45	0.374883	0.187442	+	0.982276i	$0.439980\pi$
$618$	4616.49	0.300489
$619$	−11933.5	−0.774877	−0.387439	−	0.921896i	$-0.626640\pi$
$619$	−11933.5	−0.774877	−0.387439	+	0.921896i	$0.626640\pi$
$620$	−4225.51	−0.273711
$621$	74.2843	0.00480020
$622$	12569.7	0.810289
$623$	−2178.92	−0.140123
$624$	−3697.95	−0.237238
$625$	−6666.76	−0.426673
$626$	10876.0	0.694397
$627$	−2163.53	−0.137804
$628$	2665.31	0.169359
$629$	−4915.54	−0.311599
$630$	−243.466	−0.0153967
$631$	6555.53	0.413584	0.206792	−	0.978385i	$-0.433698\pi$
$631$	6555.53	0.413584	0.206792	+	0.978385i	$0.433698\pi$
$632$	−23328.5	−1.46829
$633$	1341.25	0.0842181
$634$	−3109.31	−0.194773
$635$	−7930.86	−0.495632
$636$	−5949.92	−0.370959
$637$	21035.3	1.30840
$638$	−4161.55	−0.258240
$639$	5244.58	0.324683
$640$	11562.1	0.714113
$641$	−11140.5	−0.686462	−0.343231	−	0.939251i	$-0.611521\pi$
$641$	−11140.5	−0.686462	−0.343231	+	0.939251i	$0.611521\pi$
$642$	−9024.01	−0.554750
$643$	5686.54	0.348764	0.174382	−	0.984678i	$-0.444207\pi$
$643$	5686.54	0.348764	0.174382	+	0.984678i	$0.444207\pi$
$644$	−36.5438	−0.00223607
$645$	−8589.91	−0.524384
$646$	−5534.53	−0.337079
$647$	14406.0	0.875360	0.437680	−	0.899131i	$-0.355800\pi$
$647$	14406.0	0.875360	0.437680	+	0.899131i	$0.355800\pi$
$648$	1606.41	0.0973856
$649$	7707.40	0.466166
$650$	−4491.22	−0.271016
$651$	545.131	0.0328193
$652$	3202.23	0.192345
$653$	19653.7	1.17781	0.588904	−	0.808203i	$-0.299560\pi$
$653$	19653.7	1.17781	0.588904	+	0.808203i	$0.299560\pi$
$654$	−6859.52	−0.410135
$655$	22021.1	1.31364
$656$	8417.41	0.500982
$657$	4740.96	0.281526
$658$	−1286.28	−0.0762074
$659$	−5237.09	−0.309572	−0.154786	−	0.987948i	$-0.549469\pi$
$659$	−5237.09	−0.309572	−0.154786	+	0.987948i	$0.549469\pi$
$660$	1701.48	0.100349
$661$	21498.8	1.26506	0.632531	−	0.774535i	$-0.282016\pi$
$661$	21498.8	1.26506	0.632531	+	0.774535i	$0.282016\pi$
$662$	1592.67	0.0935060
$663$	−11115.8	−0.651136
$664$	−3210.59	−0.187643
$665$	1251.14	0.0729582
$666$	1053.06	0.0612694
$667$	−734.274	−0.0426255
$668$	8172.15	0.473338
$669$	11156.6	0.644753
$670$	6355.36	0.366461
$671$	671.000	0.0386046
$672$	−1242.15	−0.0713053
$673$	7905.25	0.452786	0.226393	−	0.974036i	$-0.427307\pi$
$673$	7905.25	0.452786	0.226393	+	0.974036i	$0.427307\pi$
$674$	9960.75	0.569249
$675$	−1374.89	−0.0783991
$676$	−10029.6	−0.570641
$677$	−4578.36	−0.259913	−0.129956	−	0.991520i	$-0.541484\pi$
$677$	−4578.36	−0.259913	−0.129956	+	0.991520i	$0.541484\pi$
$678$	−2498.24	−0.141511
$679$	−3117.28	−0.176186
$680$	10165.2	0.573258
$681$	−14564.5	−0.819550
$682$	1277.90	0.0717496
$683$	−23522.2	−1.31779	−0.658895	−	0.752235i	$-0.728976\pi$
$683$	−23522.2	−1.31779	−0.658895	+	0.752235i	$0.728976\pi$
$684$	−3534.75	−0.197594
$685$	15617.6	0.871121
$686$	2140.67	0.119142
$687$	−8974.50	−0.498397
$688$	−6590.78	−0.365220
$689$	−20599.0	−1.13898
$690$	−100.702	−0.00555601
$691$	29259.9	1.61086	0.805428	−	0.592694i	$-0.201936\pi$
$691$	29259.9	1.61086	0.805428	+	0.592694i	$0.201936\pi$
$692$	5485.91	0.301363
$693$	−219.507	−0.0120323
$694$	8798.49	0.481248
$695$	3265.35	0.178218
$696$	−15878.8	−0.864778
$697$	25302.3	1.37502
$698$	−2680.61	−0.145362
$699$	−16295.4	−0.881758
$700$	676.369	0.0365205
$701$	−24217.3	−1.30482	−0.652408	−	0.757868i	$-0.726241\pi$
$701$	−24217.3	−1.30482	−0.652408	+	0.757868i	$0.726241\pi$
$702$	2381.36	0.128032
$703$	−5411.57	−0.290329
$704$	−1168.46	−0.0625540
$705$	10567.0	0.564506
$706$	14166.0	0.755164
$707$	−220.896	−0.0117505
$708$	12592.3	0.668428
$709$	−5091.43	−0.269693	−0.134847	−	0.990866i	$-0.543054\pi$
$709$	−5091.43	−0.269693	−0.134847	+	0.990866i	$0.543054\pi$
$710$	−7109.69	−0.375805
$711$	−10586.6	−0.558410
$712$	−19489.5	−1.02584
$713$	225.476	0.0118431
$714$	−561.523	−0.0294320
$715$	5890.64	0.308108
$716$	5168.43	0.269767
$717$	15666.3	0.815997
$718$	12712.0	0.660736
$719$	−18989.5	−0.984966	−0.492483	−	0.870322i	$-0.663911\pi$
$719$	−18989.5	−0.984966	−0.492483	+	0.870322i	$0.663911\pi$
$720$	1534.63	0.0794336
$721$	−2406.95	−0.124326
$722$	3629.92	0.187107
$723$	−21141.7	−1.08751
$724$	−5776.35	−0.296514
$725$	13590.3	0.696179
$726$	−514.569	−0.0263050
$727$	−19270.4	−0.983082	−0.491541	−	0.870854i	$-0.663566\pi$
$727$	−19270.4	−0.983082	−0.491541	+	0.870854i	$0.663566\pi$
$728$	−2735.96	−0.139288
$729$	729.000	0.0370370
$730$	−6426.97	−0.325853
$731$	−19811.5	−1.00240
$732$	1096.27	0.0553544
$733$	722.954	0.0364296	0.0182148	−	0.999834i	$-0.494202\pi$
$733$	722.954	0.0364296	0.0182148	+	0.999834i	$0.494202\pi$
$734$	−7256.05	−0.364885
$735$	−8729.54	−0.438087
$736$	−513.777	−0.0257311
$737$	5729.95	0.286384
$738$	−5420.55	−0.270370
$739$	4829.80	0.240416	0.120208	−	0.992749i	$-0.461644\pi$
$739$	4829.80	0.240416	0.120208	+	0.992749i	$0.461644\pi$
$740$	4255.87	0.211418
$741$	−12237.5	−0.606689
$742$	−1040.57	−0.0514833
$743$	20581.7	1.01625	0.508123	−	0.861285i	$-0.330340\pi$
$743$	20581.7	1.01625	0.508123	+	0.861285i	$0.330340\pi$
$744$	4875.96	0.240270
$745$	−26756.2	−1.31580
$746$	12143.1	0.595966
$747$	−1456.98	−0.0713631
$748$	3924.25	0.191825
$749$	4704.94	0.229526
$750$	6439.07	0.313495
$751$	23843.5	1.15854	0.579269	−	0.815137i	$-0.303338\pi$
$751$	23843.5	1.15854	0.579269	+	0.815137i	$0.303338\pi$
$752$	8107.75	0.393164
$753$	−5405.34	−0.261596
$754$	−23538.9	−1.13692
$755$	−20359.7	−0.981413
$756$	−358.628	−0.0172529
$757$	−3431.10	−0.164736	−0.0823682	−	0.996602i	$-0.526248\pi$
$757$	−3431.10	−0.164736	−0.0823682	+	0.996602i	$0.526248\pi$
$758$	−4077.73	−0.195395
$759$	−90.7919	−0.00434195
$760$	11190.9	0.534128
$761$	−7314.05	−0.348402	−0.174201	−	0.984710i	$-0.555734\pi$
$761$	−7314.05	−0.348402	−0.174201	+	0.984710i	$0.555734\pi$
$762$	3918.62	0.186295
$763$	3576.42	0.169692
$764$	4799.98	0.227300
$765$	4613.01	0.218018
$766$	−4784.82	−0.225695
$767$	43595.3	2.05233
$768$	−8262.17	−0.388197
$769$	22593.2	1.05947	0.529733	−	0.848164i	$-0.322292\pi$
$769$	22593.2	1.05947	0.529733	+	0.848164i	$0.322292\pi$
$770$	297.569	0.0139268
$771$	205.000	0.00957575
$772$	17687.5	0.824596
$773$	12071.8	0.561697	0.280849	−	0.959752i	$-0.409384\pi$
$773$	12071.8	0.561697	0.280849	+	0.959752i	$0.409384\pi$
$774$	4244.26	0.197102
$775$	−4173.20	−0.193427
$776$	−27882.7	−1.28986
$777$	−549.047	−0.0253500
$778$	11867.9	0.546898
$779$	27855.5	1.28117
$780$	9624.07	0.441791
$781$	−6410.04	−0.293687
$782$	−232.256	−0.0106208
$783$	−7205.91	−0.328887
$784$	−6697.91	−0.305116
$785$	−3829.36	−0.174109
$786$	−10880.6	−0.493761
$787$	27192.4	1.23164	0.615822	−	0.787885i	$-0.288824\pi$
$787$	27192.4	1.23164	0.615822	+	0.787885i	$0.288824\pi$
$788$	1763.60	0.0797281
$789$	7611.01	0.343421
$790$	14351.5	0.646334
$791$	1302.53	0.0585495
$792$	−1963.39	−0.0880886
$793$	3795.37	0.169959
$794$	−7098.56	−0.317278
$795$	8548.48	0.381363
$796$	−17575.1	−0.782577
$797$	4848.00	0.215464	0.107732	−	0.994180i	$-0.465641\pi$
$797$	4848.00	0.215464	0.107732	+	0.994180i	$0.465641\pi$
$798$	−618.186	−0.0274230
$799$	24371.5	1.07910
$800$	9509.20	0.420251
$801$	−8844.45	−0.390141
$802$	4652.11	0.204827
$803$	−5794.51	−0.254650
$804$	9361.53	0.410641
$805$	52.5039	0.00229878
$806$	7228.16	0.315882
$807$	−14675.5	−0.640151
$808$	−1975.81	−0.0860259
$809$	−33399.9	−1.45152	−0.725759	−	0.687949i	$-0.758511\pi$
$809$	−33399.9	−1.45152	−0.725759	+	0.687949i	$0.758511\pi$
$810$	−988.252	−0.0428687
$811$	−9517.74	−0.412100	−0.206050	−	0.978541i	$-0.566061\pi$
$811$	−9517.74	−0.412100	−0.206050	+	0.978541i	$0.566061\pi$
$812$	3544.92	0.153205
$813$	11296.7	0.487324
$814$	−1287.08	−0.0554202
$815$	−4600.77	−0.197740
$816$	3539.42	0.151844
$817$	−21810.7	−0.933979
$818$	−16615.6	−0.710208
$819$	−1241.60	−0.0529730
$820$	−21906.7	−0.932945
$821$	−18839.1	−0.800840	−0.400420	−	0.916332i	$-0.631136\pi$
$821$	−18839.1	−0.800840	−0.400420	+	0.916332i	$0.631136\pi$
$822$	−7716.62	−0.327431
$823$	18391.3	0.778957	0.389479	−	0.921036i	$-0.372655\pi$
$823$	18391.3	0.778957	0.389479	+	0.921036i	$0.372655\pi$
$824$	−21529.1	−0.910196
$825$	1680.42	0.0709147
$826$	2202.24	0.0927674
$827$	11227.7	0.472098	0.236049	−	0.971741i	$-0.424147\pi$
$827$	11227.7	0.472098	0.236049	+	0.971741i	$0.424147\pi$
$828$	−148.335	−0.00622584
$829$	21107.8	0.884324	0.442162	−	0.896935i	$-0.354212\pi$
$829$	21107.8	0.884324	0.442162	+	0.896935i	$0.354212\pi$
$830$	1975.13	0.0825995
$831$	−5346.98	−0.223207
$832$	−6609.16	−0.275398
$833$	−20133.6	−0.837439
$834$	−1613.40	−0.0669874
$835$	−11741.2	−0.486613
$836$	4320.25	0.178731
$837$	2212.74	0.0913780
$838$	10264.0	0.423105
$839$	−12984.9	−0.534314	−0.267157	−	0.963653i	$-0.586084\pi$
$839$	−12984.9	−0.534314	−0.267157	+	0.963653i	$0.586084\pi$
$840$	1135.41	0.0466373
$841$	46838.9	1.92049
$842$	16071.5	0.657791
$843$	19641.3	0.802468
$844$	−2678.29	−0.109231
$845$	14409.9	0.586645
$846$	−5221.14	−0.212183
$847$	268.286	0.0108836
$848$	6558.99	0.265609
$849$	−3173.27	−0.128276
$850$	4298.69	0.173463
$851$	−227.096	−0.00914775
$852$	−10472.7	−0.421112
$853$	49060.2	1.96927	0.984636	−	0.174620i	$-0.0558695\pi$
$853$	49060.2	1.96927	0.984636	+	0.174620i	$0.0558695\pi$
$854$	191.726	0.00768233
$855$	5078.51	0.203136
$856$	42083.7	1.68036
$857$	5939.31	0.236736	0.118368	−	0.992970i	$-0.462234\pi$
$857$	5939.31	0.236736	0.118368	+	0.992970i	$0.462234\pi$
$858$	−2910.55	−0.115810
$859$	−34360.8	−1.36481	−0.682407	−	0.730973i	$-0.739067\pi$
$859$	−34360.8	−1.36481	−0.682407	+	0.730973i	$0.739067\pi$
$860$	17152.8	0.680123
$861$	2826.17	0.111865
$862$	23917.5	0.945050
$863$	−12675.6	−0.499981	−0.249991	−	0.968248i	$-0.580428\pi$
$863$	−12675.6	−0.499981	−0.249991	+	0.968248i	$0.580428\pi$
$864$	−5042.02	−0.198534
$865$	−7881.82	−0.309815
$866$	11852.0	0.465066
$867$	−4099.69	−0.160591
$868$	−1088.55	−0.0425665
$869$	12939.2	0.505101
$870$	9768.52	0.380671
$871$	32410.2	1.26083
$872$	31989.5	1.24232
$873$	−12653.3	−0.490551
$874$	−255.693	−0.00989581
$875$	−3357.21	−0.129708
$876$	−9467.01	−0.365138
$877$	−43430.2	−1.67222	−0.836108	−	0.548565i	$-0.815174\pi$
$877$	−43430.2	−1.67222	−0.836108	+	0.548565i	$0.815174\pi$
$878$	9012.68	0.346427
$879$	−1717.78	−0.0659150
$880$	−1875.65	−0.0718504
$881$	−25569.3	−0.977811	−0.488905	−	0.872337i	$-0.662604\pi$
$881$	−25569.3	−0.977811	−0.488905	+	0.872337i	$0.662604\pi$
$882$	4313.24	0.164665
$883$	−4597.02	−0.175201	−0.0876003	−	0.996156i	$-0.527920\pi$
$883$	−4597.02	−0.175201	−0.0876003	+	0.996156i	$0.527920\pi$
$884$	22196.7	0.844520
$885$	−18091.8	−0.687175
$886$	24109.4	0.914189
$887$	29068.7	1.10037	0.550187	−	0.835042i	$-0.314557\pi$
$887$	29068.7	1.10037	0.550187	+	0.835042i	$0.314557\pi$
$888$	−4910.99	−0.185588
$889$	−2043.09	−0.0770789
$890$	11989.8	0.451571
$891$	−891.000	−0.0335013
$892$	−22278.1	−0.836241
$893$	26830.8	1.00544
$894$	13220.2	0.494574
$895$	−7425.68	−0.277333
$896$	2978.55	0.111056
$897$	−513.546	−0.0191157
$898$	−14770.7	−0.548890
$899$	−21872.1	−0.811431
$900$	2745.45	0.101683
$901$	19716.0	0.729006
$902$	6625.11	0.244559
$903$	−2212.87	−0.0815502
$904$	11650.6	0.428642
$905$	8299.11	0.304831
$906$	10059.7	0.368886
$907$	−24736.7	−0.905587	−0.452794	−	0.891615i	$-0.649573\pi$
$907$	−24736.7	−0.905587	−0.452794	+	0.891615i	$0.649573\pi$
$908$	29083.2	1.06295
$909$	−896.636	−0.0327168
$910$	1683.14	0.0613138
$911$	−1133.09	−0.0412083	−0.0206042	−	0.999788i	$-0.506559\pi$
$911$	−1133.09	−0.0412083	−0.0206042	+	0.999788i	$0.506559\pi$
$912$	3896.58	0.141479
$913$	1780.76	0.0645504
$914$	−518.285	−0.0187564
$915$	−1575.06	−0.0569069
$916$	17920.8	0.646418
$917$	5672.91	0.204292
$918$	−2279.28	−0.0819470
$919$	17589.7	0.631370	0.315685	−	0.948864i	$-0.397766\pi$
$919$	17589.7	0.631370	0.315685	+	0.948864i	$0.397766\pi$
$920$	469.625	0.0168294
$921$	−372.712	−0.0133347
$922$	8623.82	0.308037
$923$	−36257.1	−1.29297
$924$	438.324	0.0156058
$925$	4203.18	0.149405
$926$	7532.27	0.267306
$927$	−9770.03	−0.346160
$928$	49838.6	1.76297
$929$	28062.9	0.991081	0.495541	−	0.868585i	$-0.334970\pi$
$929$	28062.9	0.991081	0.495541	+	0.868585i	$0.334970\pi$
$930$	−2999.65	−0.105766
$931$	−22165.2	−0.780275
$932$	32539.6	1.14364
$933$	−26601.7	−0.933442
$934$	13429.7	0.470486
$935$	−5638.12	−0.197204
$936$	−11105.5	−0.387816
$937$	−43554.9	−1.51854	−0.759272	−	0.650773i	$-0.774445\pi$
$937$	−43554.9	−1.51854	−0.759272	+	0.650773i	$0.774445\pi$
$938$	1637.22	0.0569907
$939$	−23017.3	−0.799936
$940$	−21100.8	−0.732162
$941$	48889.9	1.69369	0.846847	−	0.531836i	$-0.178498\pi$
$941$	48889.9	1.69369	0.846847	+	0.531836i	$0.178498\pi$
$942$	1892.08	0.0654429
$943$	1168.95	0.0403673
$944$	−13881.3	−0.478599
$945$	515.255	0.0177368
$946$	−5187.42	−0.178285
$947$	687.312	0.0235846	0.0117923	−	0.999930i	$-0.496246\pi$
$947$	687.312	0.0235846	0.0117923	+	0.999930i	$0.496246\pi$
$948$	21139.9	0.724255
$949$	−32775.4	−1.12111
$950$	4732.47	0.161623
$951$	6580.33	0.224376
$952$	2618.67	0.0891510
$953$	−13679.3	−0.464969	−0.232484	−	0.972600i	$-0.574685\pi$
$953$	−13679.3	−0.464969	−0.232484	+	0.972600i	$0.574685\pi$
$954$	−4223.79	−0.143344
$955$	−6896.32	−0.233675
$956$	−31283.4	−1.05834
$957$	8807.22	0.297489
$958$	−13964.6	−0.470956
$959$	4023.30	0.135473
$960$	2742.76	0.0922107
$961$	−23074.7	−0.774551
$962$	−7280.09	−0.243991
$963$	19097.8	0.639064
$964$	42216.9	1.41049
$965$	−25412.3	−0.847723
$966$	−25.9421	−0.000864050 0
$967$	38268.0	1.27261	0.636307	−	0.771436i	$-0.280461\pi$
$967$	38268.0	1.27261	0.636307	+	0.771436i	$0.280461\pi$
$968$	2399.70	0.0796791
$969$	11712.9	0.388311
$970$	17153.2	0.567790
$971$	−32825.7	−1.08489	−0.542444	−	0.840092i	$-0.682501\pi$
$971$	−32825.7	−1.08489	−0.542444	+	0.840092i	$0.682501\pi$
$972$	−1455.71	−0.0480369
$973$	841.195	0.0277158
$974$	−83.5911	−0.00274993
$975$	9504.93	0.312206
$976$	−1208.49	−0.0396342
$977$	−17925.6	−0.586993	−0.293497	−	0.955960i	$-0.594819\pi$
$977$	−17925.6	−0.586993	−0.293497	+	0.955960i	$0.594819\pi$
$978$	2273.23	0.0743250
$979$	10809.9	0.352896
$980$	17431.6	0.568196
$981$	14517.0	0.472470
$982$	−12160.6	−0.395175
$983$	37835.1	1.22762	0.613811	−	0.789453i	$-0.289636\pi$
$983$	37835.1	1.22762	0.613811	+	0.789453i	$0.289636\pi$
$984$	25278.8	0.818963
$985$	−2533.83	−0.0819641
$986$	22529.8	0.727684
$987$	2722.20	0.0877898
$988$	24436.6	0.786873
$989$	−915.283	−0.0294280
$990$	1207.86	0.0387762
$991$	−7297.04	−0.233903	−0.116952	−	0.993138i	$-0.537312\pi$
$991$	−7297.04	−0.233903	−0.116952	+	0.993138i	$0.537312\pi$
$992$	−15304.1	−0.489824
$993$	−3370.63	−0.107718
$994$	−1831.55	−0.0584438
$995$	25250.8	0.804526
$996$	2909.39	0.0925576
$997$	−23683.3	−0.752316	−0.376158	−	0.926556i	$-0.622755\pi$
$997$	−23683.3	−0.752316	−0.376158	+	0.926556i	$0.622755\pi$
$998$	20731.9	0.657571
$999$	−2228.64	−0.0705815

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.c.1.15	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.c.1.15	✓	37	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-1.41755 q^{2} +3.00000 q^{3} -5.99056 q^{4} +8.60687 q^{5} -4.25264 q^{6} +2.21724 q^{7} +19.8323 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.41755 q^{2} +3.00000 q^{3} -5.99056 q^{4} +8.60687 q^{5} -4.25264 q^{6} +2.21724 q^{7} +19.8323 q^{8} +9.00000 q^{9} -12.2006 q^{10} -11.0000 q^{11} -17.9717 q^{12} -62.2192 q^{13} -3.14304 q^{14} +25.8206 q^{15} +19.8114 q^{16} +59.5520 q^{17} -12.7579 q^{18} +65.5614 q^{19} -51.5600 q^{20} +6.65173 q^{21} +15.5930 q^{22} +2.75127 q^{23} +59.4968 q^{24} -50.9217 q^{25} +88.1986 q^{26} +27.0000 q^{27} -13.2825 q^{28} -266.886 q^{29} -36.6019 q^{30} +81.9533 q^{31} -186.742 q^{32} -33.0000 q^{33} -84.4176 q^{34} +19.0835 q^{35} -53.9151 q^{36} -82.5421 q^{37} -92.9362 q^{38} -186.658 q^{39} +170.694 q^{40} +424.877 q^{41} -9.42913 q^{42} -332.676 q^{43} +65.8962 q^{44} +77.4619 q^{45} -3.90005 q^{46} +409.247 q^{47} +59.4341 q^{48} -338.084 q^{49} +72.1839 q^{50} +178.656 q^{51} +372.728 q^{52} +331.072 q^{53} -38.2737 q^{54} -94.6756 q^{55} +43.9729 q^{56} +196.684 q^{57} +378.322 q^{58} -700.673 q^{59} -154.680 q^{60} -61.0000 q^{61} -116.172 q^{62} +19.9552 q^{63} +106.224 q^{64} -535.513 q^{65} +46.7790 q^{66} -520.904 q^{67} -356.750 q^{68} +8.25381 q^{69} -27.0518 q^{70} +582.731 q^{71} +178.490 q^{72} +526.774 q^{73} +117.007 q^{74} -152.765 q^{75} -392.750 q^{76} -24.3897 q^{77} +264.596 q^{78} -1176.29 q^{79} +170.514 q^{80} +81.0000 q^{81} -602.283 q^{82} -161.887 q^{83} -39.8476 q^{84} +512.556 q^{85} +471.584 q^{86} -800.657 q^{87} -218.155 q^{88} -982.716 q^{89} -109.806 q^{90} -137.955 q^{91} -16.4817 q^{92} +245.860 q^{93} -580.126 q^{94} +564.278 q^{95} -560.225 q^{96} -1405.93 q^{97} +479.249 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9}+O(q^{10}) \) 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9	\( 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9} - 41 q^{10} - 407 q^{11} + 390 q^{12} + 51 q^{13} - 228 q^{14} - 105 q^{15} + 462 q^{16} - 190 q^{17} - 72 q^{18} - 51 q^{19} - 720 q^{20} - 105 q^{21} + 88 q^{22} - 583 q^{23} - 351 q^{24} + 598 q^{25} - 1019 q^{26} + 999 q^{27} - 498 q^{28} - 566 q^{29} - 123 q^{30} - 696 q^{31} - 859 q^{32} - 1221 q^{33} - 348 q^{34} - 1102 q^{35} + 1170 q^{36} - 1022 q^{37} - 455 q^{38} + 153 q^{39} - 503 q^{40} - 790 q^{41} - 684 q^{42} - 87 q^{43} - 1430 q^{44} - 315 q^{45} - 303 q^{46} - 1603 q^{47} + 1386 q^{48} + 110 q^{49} - 1926 q^{50} - 570 q^{51} + 736 q^{52} - 2619 q^{53} - 216 q^{54} + 385 q^{55} - 4937 q^{56} - 153 q^{57} - 1099 q^{58} - 2471 q^{59} - 2160 q^{60} - 2257 q^{61} - 2909 q^{62} - 315 q^{63} - 265 q^{64} - 1970 q^{65} + 264 q^{66} - 3033 q^{67} - 1956 q^{68} - 1749 q^{69} + 2410 q^{70} - 3891 q^{71} - 1053 q^{72} + 391 q^{73} - 532 q^{74} + 1794 q^{75} + 1554 q^{76} + 385 q^{77} - 3057 q^{78} + 67 q^{79} - 5111 q^{80} + 2997 q^{81} - 4818 q^{82} - 5315 q^{83} - 1494 q^{84} - 2747 q^{85} - 5195 q^{86} - 1698 q^{87} + 1287 q^{88} - 8945 q^{89} - 369 q^{90} - 4432 q^{91} - 4701 q^{92} - 2088 q^{93} - 372 q^{94} - 3388 q^{95} - 2577 q^{96} - 3784 q^{97} - 4502 q^{98} - 3663 q^{99}+O(q^{100}) \) 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9 - 41 * q^10 - 407 * q^11 + 390 * q^12 + 51 * q^13 - 228 * q^14 - 105 * q^15 + 462 * q^16 - 190 * q^17 - 72 * q^18 - 51 * q^19 - 720 * q^20 - 105 * q^21 + 88 * q^22 - 583 * q^23 - 351 * q^24 + 598 * q^25 - 1019 * q^26 + 999 * q^27 - 498 * q^28 - 566 * q^29 - 123 * q^30 - 696 * q^31 - 859 * q^32 - 1221 * q^33 - 348 * q^34 - 1102 * q^35 + 1170 * q^36 - 1022 * q^37 - 455 * q^38 + 153 * q^39 - 503 * q^40 - 790 * q^41 - 684 * q^42 - 87 * q^43 - 1430 * q^44 - 315 * q^45 - 303 * q^46 - 1603 * q^47 + 1386 * q^48 + 110 * q^49 - 1926 * q^50 - 570 * q^51 + 736 * q^52 - 2619 * q^53 - 216 * q^54 + 385 * q^55 - 4937 * q^56 - 153 * q^57 - 1099 * q^58 - 2471 * q^59 - 2160 * q^60 - 2257 * q^61 - 2909 * q^62 - 315 * q^63 - 265 * q^64 - 1970 * q^65 + 264 * q^66 - 3033 * q^67 - 1956 * q^68 - 1749 * q^69 + 2410 * q^70 - 3891 * q^71 - 1053 * q^72 + 391 * q^73 - 532 * q^74 + 1794 * q^75 + 1554 * q^76 + 385 * q^77 - 3057 * q^78 + 67 * q^79 - 5111 * q^80 + 2997 * q^81 - 4818 * q^82 - 5315 * q^83 - 1494 * q^84 - 2747 * q^85 - 5195 * q^86 - 1698 * q^87 + 1287 * q^88 - 8945 * q^89 - 369 * q^90 - 4432 * q^91 - 4701 * q^92 - 2088 * q^93 - 372 * q^94 - 3388 * q^95 - 2577 * q^96 - 3784 * q^97 - 4502 * q^98 - 3663 * q^99

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